Math 3081 (Probability and Statistics), Summer-II 2021
| Course Information | |||||
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| Instructor | Class Times | Office Hours | |||
| Evan Dummit edummit at northeastern dot edu |
(Section 1) MTWR, 1:30pm-3:10pm (Section 2) MTWR, 9:50am-11:30am Online, via Zoom |
M 3:15pm-4:30pm R 3:15pm-4:30pm or by appointment Online, via Zoom |
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| There are two sections of Math 3081, corresponding to the two lecture times listed. The lectures will cover the same material at the same pace. All lectures will be recorded and made available for on-demand viewing at any time. | |||||
| Math 3081 uses a Piazza page for course discussion. Links to all of the live lectures, office hours, problem sessions, and lecture recordings are hosted there. | |||||
| Teaching Assistant | Recitation Time | Office Hours | |||
| Jiewei Feng feng.ji at northeastern dot edu |
R noon-1pm Online, via Zoom |
T 3:30pm-4:30pm Online, via Zoom |
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| For detailed information about the course, please consult the 3081 Course Syllabus. (Note: any information given in class or on this webpage supersedes the written syllabus.) | |||||
| All homework assignments are available on the 3081 WeBWorK page. To create your initial login, follow the Rederly signup link posted on the 3081 Canvas page (you must use your Northeastern email address). | |||||
| Handouts / Lecture Notes | |||||
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| The instructor will write lecture notes for the course in place of an official textbook as the semester progresses. The course will follow the presentation in Larsen and Marx's "An Introduction to Mathematical Statistics and its Applications" (5th edition), but it is not necessary to purchase the textbook for this course. For those students who are using the textbook, here are the correspondences between the notes and textbook: Notes ch1: Book §2.1-2.7 (Probability) Notes ch2: Book §3.1-3.9 + §4.1-4.3 (Random Variables) Notes ch3: Book §5.1-5.4 (Parameter Estimation) Notes ch4: Book §6.1-6.4 + §7.1-7.5 (Hypothesis Testing) Notes ch5: Book §9.1-9.5 + §10.1-10.4 (Topics in Hypothesis Testing) |
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| Handout | Topics | ||||
| Chapter 1: Counting and Probability (25pp, v2.50, posted 6/29) | 1.1 ~ Sets and Set Operations 1.2 ~ Counting Principles 1.3 ~ Probability and Probability Distributions 1.4 ~ Conditional Probability and Independence |
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| Chapter 2: Random Variables (36pp, v2.50, posted 7/9) | 2.1 ~ Discrete Random Variables 2.2 ~ Continuous Random Variables 2.3 ~ The Normal Distribution, Central Limit Theorem, and Modeling Applications |
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| Chapter 3: Parameter and Interval Estimation (18pp, v2.00, posted 7/24) | 3.1 ~ Parameter Estimation 3.2 ~ Interval Estimation |
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| Chapter 4: Hypothesis Testing (21pp, v2.00, posted 8/1) | 4.1 ~ Principles of Hypothesis Testing 4.2 ~ One-Sample and Two-Sample z Tests 4.3 ~ Errors and Misinterpretations of Hypothesis Testing |
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| Chapter 5: Topics in Hypothesis Testing (31pp, v2.00, posted 8/7) | 5.1 ~ The t Distribution and t Tests 5.2 ~ The χ2 Distribution and χ2 Tests |
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| Lecture Slides | |||
|---|---|---|---|
| These are the slides used during the lectures. They will usually be posted ahead of the lecture time. | |||
| Date | Material | ||
| Mon, Jul 5th Tue, Jul 6th Wed, Jul 7th Thu, Jul 8th |
University holiday; no classes
Lecture 1: Welcome + Sets and Counting (Notes 1.1-1.2.1) [typos fixed] Lecture 2: Permutations and Combinations, Sample Spaces (Notes 1.2.2-1.3.1) Lecture 3: Probability (Notes 1.3.2-1.3.3) |
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| Mon, Jul 12th Tue, Jul 13th Wed, Jul 14th Thu, Jul 15th |
Lecture 4: Conditional Probability and Independence (Notes 1.3.3-1.4.1)
Lecture 5: Computing Probabilities (Notes 1.4.2-1.4.3) Lecture 6: Bayes' Theorem + Discrete Random Variables (Notes 1.4.3 + 2.1.1-2.1.2) Lecture 7: Discrete Random Variables, Part 2 (Notes 2.1.3-2.1.5) |
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| Mon, Jul 19th Tue, Jul 20th Wed, Jul 21st Thu, Jul 22nd |
Lecture 8: Discrete Random Variables, Part 3 (Notes 2.1.5-2.2.2)
Lecture 9: Continuous Random Variables, Part 1.5 (Notes 2.2.1-2.2.2) Lecture 10: Continuous Random Variables, Part 2.5 (Notes 2.2.2-2.2.3) [updated] Lecture 11: Continuous Random Variables, Part 3.5 + Normal Distributions (Notes 2.2.4-2.3.2) |
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| Mon, Jul 26th Tue, Jul 27th Wed, Jul 28th Thu, Jul 29th |
Lecture 12: The Central Limit Theorem and Applications (Notes 2.3.2-2.3.3)
Lecture 13: Poisson + Exponential Applications (Notes 2.3.3-2.3.4) Lecture 14: Maximum Likelihood Estimates (Notes 3.1.1-3.1.2) Lecture 15: Bias and Efficiency of Estimators (Notes 3.1.2-3.1.3) |
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| Mon, Aug 2nd Tue, Aug 3rd Wed, Aug 4th Thu, Aug 5th |
Lecture 16: Confidence Intervals, Part 1 (Notes 3.2.1-3.2.2)
Lecture 17: Confidence Intervals, Part 2 (Notes 3.2.2-3.2.3) Lecture 18: Hypothesis Testing, z-Tests (Notes 4.1.1-4.2.1) [typos fixed] Lecture 19: More z-Tests (Notes 4.2.1-4.2.3) |
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| Mon, Aug 9th Tue, Aug 10th Wed, Aug 11th Thu, Aug 12th |
Lecture 20: Unknown Proportion + Errors in Hypothesis Testing (Notes 4.2.3-4.3.1)
Lecture 21: Errors and Misuses of Hypothesis Testing (Notes 4.3.1-4.3.2) Lecture 22: The t Distribution and Confidence Intervals (Notes 5.1.1-5.1.2) Lecture 23: One-Sample t Tests (Notes 5.1.3-5.1.4) |
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| Mon, Aug 16th Tue, Aug 17th Wed, Aug 18th Thu, Aug 19th |
Lecture 24: Two-Sample t Tests (Notes 5.1.4)
Lecture 25: Matched Pairs + Robustness of t Tests (Notes 5.1.4-5.1.5) Lecture 26: The χ2 Distribution and Confidence Intervals (Notes 5.2.1-5.2.3) Lecture 27: The χ2 Tests for Goodness of Fit and Independence (Notes 5.2.3-5.2.4) |
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| Problem Sheets | |||
|---|---|---|---|
| These are the problem sheets for the course's problem sessions, held each week on Thursday. | |||
| Date | Material | ||
| Thu, Jul 8th | Session 1 (Sets, Counting, and Probability): Sheet 1, Sheet 1a | ||
| Thu, Jul 15th | Session 2 (Probability and Discrete Random Variables): Sheet 2 | ||
| Thu, Jul 22nd | Session 3 (Discrete and Continuous Random Variables): Sheet 3 | ||
| Thu, Jul 29th | Session 4 (Continuous Variables, Normal, Exponential, Poisson): Sheet 4 | ||
| Thu, Aug 5th | Session 5 (MLEs, Bias + Efficiency, Confidence Intervals): Sheet 5 | ||
| Thu, Aug 12th | Session 6 (Hypothesis Tests, z tests, Type I/II Errors, Power): Sheet 6 | ||
| Thu, Aug 19th | Session 7 (t and χ2 Tests + Confidence Intervals): Sheet 7 | ||
| Exam Information | ||||
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| Exams will be distributed and collected via the 3081 Canvas page. You will download the exam file, take it, and then upload scans of your exam responses during your testing window. | ||||
| Exam | Date, Time, Location | Topics | Review Material | |
| Exam 1 (Form A), (sols) (Form B), (sols) |
Sat, Jul 17th Via Canvas |
Lectures 1-7 WeBWorKs 1-2 Notes §1.1-1.4 + §2.1.1-2.1.3 |
Review Problems (answers) Review session Fri Jul 16th, 1pm-3pm |
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| Exam 2 (Form A), (sols) (Form B), (sols) |
Sat, Jul 31st Via Canvas |
Lectures 8-14 WeBWorKs 3-4 Notes §2.1-2.3 |
Review Problems (answers) Review session Fri Jul 30th, 1pm-3pm |
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| Exam 3 (Form A), (sols) (Form B), (sols) |
Sat, Aug 14th Via Canvas |
Lectures 15-22 WeBWorKs 5-6 Notes §3.1-3.2 + §4.1-4.2.2 + §5.1.-5.1.2 |
Review Problems (answers) Review session Fri Aug 13th, 1pm-3pm |
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| Final | Mon, Aug 23rd or Tue, Aug 24th Via Canvas |
Comprehensive: Lectures 1-27 WeBWorKs 1-7 Notes §1.1-5.2 |
Short: Lectures 23-27 WeBWorK 7 Notes §5.1-5.2 |
Review Problems (answers) Review sessions Sat Aug 21st + Sun Aug 22nd, times TBA |
| For exams, you are permitted one "cheat sheet", consisting of a single-sided 8.5in-by-11in piece of paper. Calculators are permitted, but cell phones, other electronic devices, books, and additional notes of any kind will NOT be permitted in exams. | ||||
| Old Exams | |||
|---|---|---|---|
| These are exams from previous Math 3081 courses, and are provided to give you an additional source of practice problems. Please note: some courses may have been organized differently than this course, so some material may differ from exam to exam. Some topics from our course may be covered or emphasized differently, or skipped altogether, and some topics on these exams may not appear on the exams in this course. | |||
| Exam 1 | Exam 2 | Exam 3 | Final Exam |
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2018 Summer 1 (with solutions) 2019 Summer 2, (solutions) |
2018 Summer 1, (solutions) 2019 Summer 2, (solutions) |
2018 Summer 1, (solutions) 2019 Summer 2, (solutions) |
2017 Spring, (solutions) 2017 Spring, (solutions) 2017 Spring, (solutions) 2017 Summer 2 (with solutions) 2018 Spring, (solutions) 2018 Summer 1, (solutions) |
| Tips For Success In This Course | |||
|---|---|---|---|
| Attend Lecture | Missing lecture is a bad idea! If for any reason you cannot make it to a class, you should watch the recording of the lecture. You are responsible for all material covered in lecture. | ||
| Read the Lecture Notes (or Textbook) | The lecture notes and the textbook are comprehensive sources of material for the course. The notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes are not identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material. | ||
| Use WeBWorK Effectively | WeBWorK assignments are intended to help you learn the course material at a basic level. Look over the problems well before the due date, and work on them in concert with the corresponding lectures. You may use technology (calculators, Wolfram Alpha, computer software) and other people to help you (so long as you are submitting your own work), but be mindful: if you do not understand how to do the WeBWorK problems, you will almost certainly struggle on the exams! (Exam problems are often harder than WeBWorK problems.) | ||
| Attend Office Hours | Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor or TAs. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with. | ||
| Use Tutoring Services | The university offers a wide variety of free tutoring services. Over the summer, the Tutoring Center is open for students taking various math courses, including Math 3081. | ||
| Course Schedule | |||
|---|---|---|---|
| The schedule is subject to change! All sections refer to the course lecture notes. | |||
| Week | Schedule | ||
| Week of July 5 (class starts 7/6) |
§1.1: Sets and Set Operations §1.2: Counting Principles §1.3: Probability and Probability Distributions §1.4.1: Conditional Probability WeBWorK 1 due Sunday 7/11 at 5am Eastern. |
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| Week of July 12 | §1.4.2: Independence §1.4.3: Computing Probabilities, Bayes' Formula §2.1.1: Discrete Random Variables §2.1.2: Expected Value §2.1.3: Variance and Standard Deviation WeBWorK 2 due Friday 7/16 at 5am Eastern. Review for Exam 1 EXAM 1 Saturday, July 17th (via Canvas) |
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| Week of July 19 | §2.1.4: Joint Distributions §2.1.5: Independence §2.1.6: Covariance and Correlation §2.2: Continuous Random Variables §2.3.1: The Normal Distribution WeBWorK 3 due Friday 7/23 at 5am Eastern. |
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| Week of July 26 |
§2.3.2: The Central Limit Theorem §2.3.3: The Poisson Distribution and Poisson Limit Theorem §2.3.4: The Exponential Distribution and Memoryless Processes §3.1.1: Maximum Likelihood Estimates §3.1.2: Biased and Unbiased Estimators WeBWorK 4 due Friday 7/30 at 5am Eastern. Review for Exam 2 EXAM 2 Saturday, July 31st (via Canvas) |
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| Week of August 2 | §3.1.3: Efficiency of Estimators §3.2.1: Confidence Intervals §3.2.2: Normal Confidence Intervals §4.1: Hypothesis Testing §4.2.1: One-Sample z Tests §4.2.2: Two-Sample z Tests WeBWorK 5 due Friday 8/6 at 5am Eastern. |
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| Week of August 9 | §4.1.3: z Tests for Unknown Proportion §4.3.1: Type I and Type II Errors §4.3.2: Misinterpretations and Misuses of Hypothesis Testing §5.1.1: The t Distributions §5.1.2: Confidence Intervals Using t Statistics §5.1.3: One-Sample t Tests WeBWorK 6 due Friday 8/13 at 5am Eastern. Review for Exam 3 EXAM 3 Saturday, August 14th (via Canvas) |
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| Week of August 16 (class ends 8/19) |
§5.1.4: Two-Sample t Tests §5.1.5: Robustness of t Tests §5.2.1: The χ2 Distributions §5.2.2: χ2 Confidence Intervals and Hypothesis Tests §5.2.3: The χ2 Test for Independence §5.2.4: The χ2 Test for Goodness of Fit WeBWorK 7 due Friday 8/20 at 5am Eastern. Review for Final Exam |
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| Week of August 17 |
FINAL EXAM Monday, August 23rd or Tuesday, August 24th (via Canvas) | ||